hight resolution digital holographic microscope and image...

Hight resolution digital holographic microscope andimage reconstruction

G. Zoltan∗†, M. Kozlovszky∗†, and L. Kovacs∗‡∗John von Neumann Faculty of Informatics, Obuda University, Budapest, Hungary

† BioTech Research Center, University Innovation and Research Center, Obuda University, Hungary‡Physiological Controls Group, University Innovation and Research Center, Obuda University, Hungary

Abstract—The current paper presents the development ofhight resolution digital holographic microscope and the picture-reconstruction software.

The application of holography is important because with it thesmall width depth of traditional microscopes can be avoidable,therefore the three dimension volume can also be reconstructed.Holography makes the examination of liquids more effective,which, for instance, can be used for many blood tests or tosupervise the quality of potable water.

I. INTRODUCTION

Currently the hologram is stabilised by a digital sensor(CCD camera), and the reconstruction is also calculated bythe numerical simulation of the expansion of light-waves. Withthis, the previously used traditional developing techniques be-come unnecessary, and it allows the completion of automatedmeasures nearly the actual time

In holography the wave nature of the light is exploited. Thelight is an electromagnetic vibration. The Maxwell equationsdescribe the interference of powers and charges and the electricand magnetic scope [1].

The interference occurs when two waves encounter; thisphenomenon is the basis of holography. The key of thisconsists that the time the hologram is stabilised, the amplitudesare accumulated. It depends on the phase difference the kindof process that the encounter of the two light waves involves.It can also happen that at the time of encounter the two lightwaves debilitate or extinguish each other. Due to the greatfrequency of illuminating light, only within the determinedintervals average of intensity can be recorded. If the differenceof phases is constant, the resultant of the two waves averageintensity of the resultant becomes constant as well. Thus, thistypical intensity rate can be seen if the rays are compassed.A stripe system evolves due to the phase difference. Thelight bars are called interference stripes. However, if thephase difference is inconstant, then the average rates are thesame in every single point, thus the emerging picture willbe continuous, homogeneous. The condition of creating aninterference picture is the constant phase difference. Thisfeature is called coherence- if the two waves are coherent,their phase difference becomes constant as well [2], [3].

During the realization of holography, the object to beimaged should be illuminated with a kind of light which iscoherent. Therefore, the laser illumination could be a goodalternative because the laser light can be considered a coherent

light, thus it gives the body to the creation of interference.Illuminating the object the amplitude and the phase of dispers-ing waves also change. These waves create the object beam.For the object beam, the reference beam should be added,which is the original illuminating light, and then it can befixed with a camera. The hologram itself is created by theinterference of these two light beams. With this technique onlythe distribution of intensity can be measured, so the calculationof the phase will be the assignment of the reconstruction.During the process of reconstruction the completed hologramshould be illuminated with a so-called restoring, reconstructingwave. In this process the interference picture only serves asa grid; the measure of the light transmission depends on theextent of the fixed intensity in every point [3], [4].

In digital holography, the fixation is made by a digitalsensor, for example a CCD camera. The reconstruction ofthe hologram is implemented by the numerical simulation ofthe expansion of light. This process also comprises takingsamples, which means that the full sign cannot be fixed, justrates in average of specific points. This might severely limitthe reconstruction of the picture [2].

Various techniques of hologram realisation are known whichallows summaing the object beam and the referent beam.Using the inline arrangement (Fig. 1.) the two beams do notseparate, so their axis falls on one straight line. One bigdrawbacks of this arrangement is that the twin pictures andthe zero ordered pictures are situated on each other on thereconstructed picture that is why it is necessary to separatethem numerically [5], [6].

Fig. 1. Inline arrangement for fixing a hologram [7].

One of the big advantages of holographic microscopy isthat the focusing can be implemented digitally, therefore theexaminable volume is much bigger, and can also be achieved amagnified picture of the examined object without magnifyinglens. The process of research and realisation becomes muchcheaper and more flexible [8].

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INES 2015 • IEEE 19th International Conference on Intelligent Engineering Systems • September 3–5, 2015, Bratislava, Slovakia

978-1-4673-7939-7/15/$31.00©2015 IEEE

The current paper presents the developement of a digitalholographic microscope which is capable producing high-definition holographic pictures of 3D objects and to createa software for the hardware by which the holographic picturescan be reconstructed. The structure of the paper is as follows:In the second paragraph, the Fresnel method in holographywill be introduced; in the third paragraph, the holographicalregistration and reconstruction will be described; the fourthparagraph reviews the development of holographic micro-scope; the fifth presents the achievements; and the sixth willsummarise the study.

II. DESCRIBING THE FRESNEL METHOD

In the following sections, the registration of the hologramwill be introduced. Let from the ff point-like light sourcedistance R the A registration plane be, which is perpendicularto axis z (Fig. 2.). The instantaneous rate of electric fieldintensity falling on the optional (y, x) point of the registrationplane is [9]:

Et(x, y) =Et0

rexp[i(kr − ωt)], (1)

where

r =√R2 + x2 + y2. (2)

As the light can be perceived only by the energy fallinginto the tracking point, therefore the energy falling into (y, x)point should be calculated, as the intensity of light [9]:

It(x, y) = E∗t (x, y)Et(x, y) =

E2t0

r2. (3)

However, if the incident intensity of light is registered,further information belonging to the incident waves phasewill be lost. For the proper tracking of the phase, a referentbeam should be made. This incident plane wave starting frompoint ff , should be coherent and identical with the light infrequency, furthermore, parallel with axis z. In this case thereferent beams phase is identical everywhere on plane A [9],[10]:

Er = Er0exp[i(kz − ωt)]|z=0 = Er0exp(−iωt). (4)

Disregarding polarisation, in point (x, y), the previouslycalculated referent beam and the wave coming from ff lightsource interfere [9]:

Et0

rexp[i(kr − ωt)] + Er0exp[−i(ωt− φ0)] =

= exp(−iωt)[Et0

rexp(ikr) + Er0exp(iφ0)],

(5)

where φ0 is the phase difference between the reference and theobject beam. Based on these, the intensities are the following[10]:

I(x, y) = E∗(x, y)E(x, y) =

=E2

t0

r2+ E2

r0 + 2Et0Er0

rcos(kr − φ0).

(6)

Fig. 2. The registration of the hologram [10].

Consequently, the incident light intensity on plane A willalso contain the modulation part of interference apart fromthe sum of intensity which derives from the two light beam.This modulation preserves quantum kr, which equals to thephase of the spherical wave which is incident on plane A(only if the two light waves are coherent and constant in φ0time). Based on these it is presumable that φ0 = 0. Hence, theintensity of the incident light changes periodically between therates (Et0/r+Er0)2 and (Et0/r−Er0)2 [10]. This period isdetermined by function cos(kr),

kδr = 2πn, n = 0, 1, 2..., (7)

As a result, we get back the same intensity on the rates [10].Hence, it could be determined where these rates are situatedon plane(x, y) [9]. According to Fig. 2. [9]:

r2 = R2 + x2 + y2 = R2 + ρ2 (8)

places with identical intensity on plane A, are situated alongconcentric circles with radius ρ. The x = y = 0 point-inintensity, which is determined by the rate of kR, appears atsuch a distance from the axis as: r −R = 2nπ/k = λ [9].

r2 −R2 = ρ2n = (r +R)(r −R) ≈ 2Rnλ, (9)

where the r+R ≈ 2R approximation should be applied. Thisapproximation holds true for every radius that is near to orclose to a small angle with the optical axis. This is calledparaxial approximation in connection with the optical calcu-lations. The obtained distribution of intensity is like placeswith identical intensity are situated along concentric circles,

G. Zoltán et al. • Hight Resolution Digital Holographic Microscope and Image Reconstruction

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and these circles radius is increasing with√n. As a result, the

condition of holography can be accomplished, which meansthat the amplitude and phase of the initial light field (thespherical wave Et) should be recorded simultaneously, if thepreviously calculated distribution of intensity is recorded. Inother words, a kind of transparency should be created whichis adequate to the distribution because of its changing capacityaccording to the location of permeability.

The achieved picture can be considered as a Fresnel type ofzone plate. Originally, according to classical optics, a Fresnelplate is a kind of transparency which has the feature that itspermeability is 1 at the previously calculated places of positivemodulations rates, so it is fully permeable; and at places withnegative modulation the permeability is 0, so it is fully capableto absorb. However, if we put the permeability as a continuousfunction, then we can achieve better result at the application ofFresnel plate. The Fresnel plate should be examined in termsof how it can restore the obtained wave field from recording,meaning that it is capable for producing the original pictureof ff point-like light source. In order to restore it, the pictureshould be illuminated with the original reference light [9], [10](Fig. 3).

Fig. 3. Diffraction on the Fresnel plate [10].

The restoring light, which is projected on the plate, i.e.on the hologram, should behave according to the rules ofdiffraction passing on the plate. Regarding Huygens principle,elemental spherical waves spring from every point of theplate where the light is transferred; the resultant light willbe the result of the interference of these spherical waves. Theillumination of the point from the plate distance R (which issituated on the axis) will be the strongest. In this point thezone plate (9), does not transfer only those waves which candeteriorate the diffracted waves falling from permeable placesthrough the process of interference. As a result, the point-like light source used at the recording can be restored if theplate is illuminated by the reference beam. On the optic axis,every (-1)st of the diffracting light crosses every diffractedlight which belongs to the diffractive order. These create adivergent light beam, the diffractive waves of the (+1)st order

adequate for these rays. However this created divergent lightsprings from the place of the original light source, so thevirtual picture of the original object can be produced with theselight beams [11]. A higher- ordered real and virtual picture canbe created from the original object with the help of the higher-ordered waves. During the process of making the hologram thedistribution of modulated intensity has to be recorded duringthe restoring process; hence higher-ordered diffractive wavescannot evolve. Furthermore, the primary ordered diffractiverays will be the biggest in intensity in comparison with thezero ordered light [12].

As a result, during the previously described process, thehologram can be created, reconstructed and restored. It can beseen that the restored holograms picture is not so ideal as itis very difficult to observe the real picture due to the picturehas been evolved as the background of the light intensity ofzero-ordered beam, which is highly intensive.

To avoid this problem, Leith and Upatnieks [13] havedeveloped the procedure that the referent beam should besituated that way that it can close any kind of angle withthe optic axis during the recording [7]. It is important that thelight used for restoration should be similarly arranged, becausethe Fresnel zone plate behaves like a lens, so the modellingcan also be accomplished with it. The Fresnel plate models therestoring light into a point on the optic axis. Subsequently, thispoint can be regarded as the focus point of the plate, namelyf = R. It is true for the picture point deriving from the primaryordered diffraction and evolving k distance from the plate that1k = 1

f −1t , so the lenses behave properly according to the

known modelling laws if the plate is illuminated with a point-like light source situated on the axis and placed t distancefrom the plate.

Applying the Frensel plate as a lens, based on (9) thefocal length is f = R = ρ21/2λ, (the first annuluss radius isexpressed with (ρ1)), so the chromatic mistake of the processcan be very big when the Fresnel plate is used for this purpose.

Regarding these conditions, the Fresnel method is tradition-ally applied for those modelling projects, where in the givenwave length those lens to be used cannot work due to strongabsorption [7], [10].

III. THE HOLOGRAPHIC REGISTRATION ANDRECONSTRUCTION

In the previous section it was mentioned that it is preferablethat the reference beams direction which is used for creatinga hologram is not identical to the optic axis. Disregarding theelectromagnetic waves time course, in this case

Rr = Er0exp[ik(R+ xsinΘ)], (10)

where Θ is the closed range of the referent beam and axis z [1].Axis x falls in the intersection of the plane of the hologram,rather the optic axis and the referent beams plane. This featurecan be seen on Fig. 4 [11].

The wave coming from the object [4]:

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Fig. 4. Restoring hologram with a referent beam out of axis [10].

Et =Et0

rexp(ikr) ≈ Et0

Rexp[ik(R+

ρ2

2R)]. (11)

Applying the paraxial approximation, the incident intensityof plane (x, y) is [4]:

I(x, y) =E2

t0

R2+E2

r0 + 2Et0Er0

Rcos[k(

ρ2

2R− xsinΘ)]. (12)

The permeability of the registered plate is [4]:

T (x, y) = K1 +K2cos[k(ρ2

2R− xsinΘ)], (13)

where K1 and K2 are constants. If it is illuminated by a planewave from under angle Θ, the rate of field strength will befrom l distance behind the plate [10].

E(ξ, η, ζ) = B

∫ ∫T (x, y)exp(−ikxsinΘ)El(ξ−x, k)dxdy,

(14)where

E(ξ − x, k) = − i

λlexp[ik(ζ +

(ξ − x)2

2l+

(η − y)2

2l)], (15)

which is called the impulse response of open field [10].Conducting the previous equations, two rectangular coordinatesystems are needed. The first is the system (x, y, z) which isfixed to the object, and the second is sytem (ξ, η, ζ) which isdefined in the picture field and its nucleus in the object fieldcan be find on place z = l [10].

In the following equations the semi-bold ξξξ = (ξ, η, ζ) andxxx = (x, y, z) mark the adequate coordinate systems vectors.Substituting these on l = R we got the following expression[10]:

E(ξ, η, ζ) = C1exp(−ikξsinΘ) +

+C2exp[ik

4R((ξ − 2RsinΘ)2 + η2)] + C3δ(ξ, η).

(16)

In (16), the first part means the zero ordered diffraction (aplane wave in parallel with the incident wave), the second partgives a concentric shaped wave front with its nucleus on theholograms illuminated side in a plane from R distance, and itfalls in a point where has coordinates (ξ = 2RsinΘ, η = 0).This result in a virtual picture. The third part of the equationgives the real picture of the object point, which can be findon the revenge side of the hologram and emerges R distancefrom it in a point with coordinates (ξ = 0, η = 0), on theoptic axis. It can be seen from previous calculations andequations that with this method the virtual picture, the realpicture and the zero ordered diffraction beam can be separated.The case have been proved by Leith and Upatnieks [13],that if we add a reference plane beam Er(x) to the wavefront Et(x, y) arriving on the surface of the shooting at anobject and we detect the resultant intensity with the beliefthat we will get a hologram as a result, then illuminated withray E∗

r (x), the reverse side of the hologram illumination, theadequate distance from the original and the real picture of theobject will be created. Instead of angle Θ, using angle −Θthe complex conjugation of referent beam can be created. Thevirtual picture of the hologram will be draw up at the originalplace of the object that the hologram should be illuminatedwith the original wave Er(x) [9], [10].

IV. DEVELOPING A HOLOGRAPHIC MICROSCOPE

In the following sections, the completed hight resolutiondigital holographic microscope will be introduced.

The reason why this device should have built is becausethere were no available holographic pictures which had theappropriate definition for the reconstruction by software; inaddition, the parameters of the found pictures were not known.For instance, one of these parameters is what can be foundin the original picture, which camera-object distance has beenused, or which wave-lenght was the illuminating light. Withoutthese parameters and skills, it is impossible to develop anaccurate reconstructional software.

A. Applied components

Fig. 5. shows the components of the digital holographicmicroscope.

The three main components of the developed device are theCCD camera, pinhole and source of light.

1) Source of light: As a source of light an RGB LEDwas applied, where the different colours light on differentwave length. Hence, the illuminating lights wave length canbe known accurately during the software developement.

2) RGB LED controller: In order to drive the controller,a separate control module was needed to switch the differentchannels of the LED separately and together as well.

3) Source of light and the pinhole: On the source oflight, a holder was put inconsistently, functioning as thepinholes socket as well. This was necessary not letting thelight escaping elsewhere but the pinhole. The pinhole wasmanufactured by Edmund Optics.

Table I contains the RGB LED’s wavelength.


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Fig. 5. The construction of the holographic microscope [2].

TABLE IRGB LED COLOURS WAVELENGTH

Color WavelengthRed 625nmGreen 525nmBlue 470nm

4) CCD camera: The produced holographic picture shouldbe fixed, for this purpose the Logitech HD Pro Webcam C910was used. Its advantage is that it has a relatively big CCDsensor.

5) The object plate: For easier testability, the pictures weremade from a USAF 1951 resolution testing plate. Fig. 6.presents the USAF 1951 plate.

Fig. 6. USAF 1951 resolution testing plate.

On the resolution testing plate, the lines are ordered ingroups, and these groups are classes. The resolution is de-termined based on the thickness of the lines.

B. Composition

At the composition it was emphasized that the distancebetween each plate could be relatively easily configured,because at the initial state for assessing these distances theplates should be often modified. Furthermore, to get a cheapdevice which is easy to be build and compiled constraints wereused on the simple materials.

TABLE IITHE IDEAL DISTANCE OF THE PLATES

The distance of light source and object beam: 3mmThe distance of object beam and CDD sensor: 13-41mm

Each plate on which the camera, the object plate and themainboard is placed are uniquely formed. These plates arefixed to each other on the corners; hence, twisting these allowsthe adjustment of the distance of the plates. On the cornersof the plates a kind of gripper is constructed which allows toconverge and abduct these by twisting the screws. In every fourcorners the distance of the plates are separately adjustable, sothe accidental gripping inaccuracy can also be corrected (Fig.7.).

Fig. 7. The finished holographic microscope, side view.

C. Operation

The operation of the device can be easily introduced. Thelight beams starting from the light source placed underneathcome through the 15µm diameter pinhole, afterwards theobject plate, and finally fall into the CCD sensor where thepicture is produced. On the LED controller the channels canbe switched individually, so the object can be illuminated withdifferent wave length lights, and later on it will be possible tomake a more detailed reconstruction.

D. Parameters

In the production of the pictures the plates with differentdistance play a main role. These distances should be set ina way that the maximum resolution can be achieved (39µm).The resolution is determined by the distance of the light sourceand the object plate, and the distance of the light source andthe camera. Table II summarizes the used distances.

V. ACHIEVEMENTS

The pictures made by the accomplished hardware have beenelaborated and reconstructed with a self-developed software.

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Examining the pictures it was turned out that the best qualityreconstruction can be achieved by pictures made with greenillumination. In green illumination the lines and the itemnumbers can also be seen much sharper. The most optimalcamera distance has been proven 13mm. In this setting thearchieved resolution became the device’s and software’s bestresolution, which is 39 micron. For the reconstruction of apicture the estimated time needed is cc. 2-3 seconds withan average, recent computer (CPU: Intel i5, RAM: 4-8GB).Nowadays, the usage of holographic picture reconstruction isaccessible, quick and simple.

Results of the USAF 1951 resolution testing plate can beseen in Fig. 8.

Fig. 8. Pictures made with 13mm camera-object distance (class 3 items 5-6).

VI. CONCLUSION

In short, the reason why the hight resolution digital holo-graphic microscope has been made is that there would be apossibility to take high-definition pictures with making pa-rameters which are known the wave-lenght of the illuminatinglight, the camera-object distance, or what the picture depicts.It was necessary for making a more accurate holographicpicture reconstruction software. In favour of the system’s

bigger resolving power, the pictures have been taken aftera USAF 1951 resolution testing sample. On the basis ofthe sample’s topology and calibration, the device’s resolvingpower can be determined, which is 39 micron in the presentedinstallation. This resolution has been archieved by the greenilluminating light, and the 13 mm camera-object distance. Boththe hardware and software of the device has been developed,by which high-definition digital holographic pictures can betaken about objects, and the original object’s virtual picturecan also be reconstructed.

VII. FURTHER WORK

Henceforth, it is planned to build a professional holographicmicroscope, which is capable for increasing the resolvingpower and each setting can be reconstructed accurately, bythe set-up of the microscope. The development of a moduleis also planned which will help taking pictures on liquidsas well. Meanwhile, further development of the software isalso planned, as in order to get a more accurate and biggerdevice in resolution numerous changes in the software areneeded. Modifications are needed to examine liquids, and thereit should be taken into consideration that the reconstructionshould be taken in a moving system, so the compensation ofthe motion should be expected.

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